NGMA 提出基于流形假设的无配对表示对齐新方法
Identifiable alignment of unpaired representations
不用配对数据也不用标签，就能把两个模型学到的表示对齐，靠的是数据本身的几何距离而不是随手选的欧氏距离。做表示分析、模型拼接或者单细胞研究的都值得看看这套 Gromov-Wasserstein 的新用法，代码思路也讲得清楚。
论文提出 Neural Gromov-Monge Alignment（NGMA），一种无需配对数据或标签的模型表示对齐方法。作者证明：在流形假设下，数据度量的 pullback 可为同一数据生成过程的任意两个模型提供共享距离，无论模型是编码器、解码器还是两者兼有，也不受架构、损失函数、先验或训练数据限制。
技术核心在于可识别性条件：当且仅当数据分布破坏数据流形上的每一个对称性时，对齐映射唯一，而论文证明这种对称性破坏在一般情形下成立。由此，对齐耦合成为 Gromov-Wasserstein 最优化的唯一解；当几乎每个数据点有 distinct 的距离分布时，线性规划单独即可达到同一最优。从置换样本中可精确恢复耦合，从独立样本中可一致估计。
实验上，NGMA 在所有无配对及标签 informed 基线中表现最优，能对齐具有不同先验的图像模型，以及在不相交细胞集上训练的单细胞模型——这些场景中欧氏距离会失效。现有方法依赖欧氏或球面几何，属于任意选择，NGMA 用 pullback 距离替代了这一假设。
Identifiable alignment of unpaired representations
Aligning two models without paired data requires a distance that both share, yet existing methods use Euclidean or spherical geometry. This is either an arbitrary choice or imposed by their loss function. We show that, under a precise form of the manifold hypothesis, the pullback of the data metric gives such a distance for any two models of one data-generating process. This holds whether the models are encoders, decoders or both, and whatever their architecture, loss, prior or training data. The alignment map preserves this distance and the distribution of representations, and is identifiable if and only if the data distribution breaks every symmetry of the data manifold. We show that this symmetry breaking holds generically. Identifiability makes the alignment coupling the unique optimum of Gromov--Wasserstein and of its weighted combinations with a linear program. The linear program alone has the same optimum if almost every data point has a distinct distribution of distances. The coupling, and with it the alignment map, is recovered exactly from permuted samples, even without identifiability, and consistently from independent ones. Our method, Neural Gromov--Monge Alignment (NGMA), uses no pairs or labels and outperforms every unpaired and label-informed baseline. It relies on pullback distances to align image models with different priors and single-cell models trained on disjoint cells, where Euclidean distances fail.
本条情报归属 AITOP「论文」核心追踪栏目。在跨区域产业观察坐标中，该动态直接关联「AI 开发者工具链、Coding Agent 与工程化实践」研究主线，反映出当前技术演进与商业落地的最新风向。涉及核心实体与技术议题包括：NGMA、Gromov-Wasserstein、表示学习、流形假设，读者可通过下方标签进入对应专题页查阅历史脉络与关联对比。
信源核验说明：本文原始线索采编自「arXiv cs.LG」（@Stas Syrota, Albert Lopez I Serrano, Johanne Franck, Søren Hauberg），经 AITOP 多维评分管线结构化提炼。